{"id":{"repo_id":"freiburg-diss","oai_identifier":"oai:freidok.uni-freiburg.de:2007"},"canonical_url":"https://search.dev.ndltd.org/etd/freiburg-diss/oai:freidok.uni-freiburg.de:2007","repository":{"repo_id":"freiburg-diss","name":"University of Freiburg","base_url":"https://freidok.uni-freiburg.de/oai/oai2.php"},"display":{"title":"Correlated dynamics of quantum wires and cigar shaped atomic gases","abstract":"In one- dimensional Fermi systems the elementary excitations,as predicted by Tomonaga- Luttinger liquid (TLL) theory, are spin and charge density waves, traveling at different velocities (the spin velocity is smaller, the charge velocity greater than the Fermi velocity). These velocities are parameters of
the TLL theory and there is no straightforward way to extract them from the parameters of a microscopic model.
But by exploiting the equivalence of the TLL ground state with the
usual electron ground state we are able to extract them from
the microscopic model's ground state energy.
In this work we investigate the dependence of charge and spin dynamics
on the interactions in different manifestations of 1D Fermi systems.
We are especially interested in the system's spin sector, which,
contrary to folklore, gets modified by electron- electron interactions.
To do so we describe the system's dynamics in terms of the TLL
while we model the interacting system's ground state with electron gas
techniques.
In quantum wires we use thermodynamical relations to obtain
the plasmon and magnon velocities from the microscopic model
and find out that the ladder approximation (LA) to the
interaction vertex faithfully follows quantum Monte Carlo data while
using a fraction of the processor time; other mean field methods,
although sometimes superior to the LA in the charge sector fail
to give meaningful results in the spin sector.
We also study the interplay of contact interaction and containment in
atomic traps, where we found out that the vanishing spin velocity
(proportional to density squared) at low densities, as predicted from Bethe
ansatz calculation, leads to a giant spin- charge separation; namely
charge density waves get reflected at the system's edge while spin density
waves experience an exponential slowing down and don't get reflected at the
trap edge.","abstract_html":"In one- dimensional Fermi systems the elementary excitations,as predicted by Tomonaga- Luttinger liquid (TLL) theory, are spin and charge density waves, traveling at different velocities (the spin velocity is smaller, the charge velocity greater than the Fermi velocity). These velocities are parameters of <br>the TLL theory and there is no straightforward way to extract them from the parameters of a microscopic model. <br>But by exploiting the equivalence of the TLL ground state with the <br>usual electron ground state we are able to extract them from <br>the microscopic model's ground state energy. <br> <br>In this work we investigate the dependence of charge and spin dynamics <br>on the interactions in different manifestations of 1D Fermi systems. <br>We are especially interested in the system's spin sector, which, <br>contrary to folklore, gets modified by electron- electron interactions. <br>To do so we describe the system's dynamics in terms of the TLL <br>while we model the interacting system's ground state with electron gas <br>techniques. <br> <br>In quantum wires we use thermodynamical relations to obtain <br>the plasmon and magnon velocities from the microscopic model <br>and find out that the ladder approximation (LA) to the <br>interaction vertex faithfully follows quantum Monte Carlo data while <br>using a fraction of the processor time; other mean field methods, <br>although sometimes superior to the LA in the charge sector fail <br>to give meaningful results in the spin sector. <br> <br>We also study the interplay of contact interaction and containment in <br>atomic traps, where we found out that the vanishing spin velocity <br>(proportional to density squared) at low densities, as predicted from Bethe <br>ansatz calculation, leads to a giant spin- charge separation; namely <br>charge density waves get reflected at the system's edge while spin density <br>waves experience an exponential slowing down and don't get reflected at the <br>trap edge.","abstract_has_math":false,"creators":["Kecke, Lars"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Grabert, Hermann"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T02:22:33Z","subjects":["Luttinger liquid"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://freidok.uni-freiburg.de/data/2007","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Grabert, Hermann"]},{"key":"dc:creator","label":"Author","values":["Kecke, Lars"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["DoctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Luttinger liquid"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In one- dimensional Fermi systems the elementary excitations,as predicted by Tomonaga- Luttinger liquid (TLL) theory, are spin and charge density waves, traveling at different velocities (the spin velocity is smaller, the charge velocity greater than the Fermi velocity). These velocities are parameters of
the TLL theory and there is no straightforward way to extract them from the parameters of a microscopic model.
But by exploiting the equivalence of the TLL ground state with the
usual electron ground state we are able to extract them from
the microscopic model's ground state energy.
In this work we investigate the dependence of charge and spin dynamics
on the interactions in different manifestations of 1D Fermi systems.
We are especially interested in the system's spin sector, which,
contrary to folklore, gets modified by electron- electron interactions.
To do so we describe the system's dynamics in terms of the TLL
while we model the interacting system's ground state with electron gas
techniques.
In quantum wires we use thermodynamical relations to obtain
the plasmon and magnon velocities from the microscopic model
and find out that the ladder approximation (LA) to the
interaction vertex faithfully follows quantum Monte Carlo data while
using a fraction of the processor time; other mean field methods,
although sometimes superior to the LA in the charge sector fail
to give meaningful results in the spin sector.
We also study the interplay of contact interaction and containment in
atomic traps, where we found out that the vanishing spin velocity
(proportional to density squared) at low densities, as predicted from Bethe
ansatz calculation, leads to a giant spin- charge separation; namely
charge density waves get reflected at the system's edge while spin density
waves experience an exponential slowing down and don't get reflected at the
trap edge.","In eindimensionalen Fermisystemen sind die elementaren Anregungen, wie von der Tomonaga-Luttinger-Flüssigkeits (TLL) Theorie vorausgesagt, Spin- und Ladungsdichtewellen die sich mit verschiedenen Geschwindigkeiten (Spindichtewellen langsamer, Ladungsdichtewellen schneller als dire Fermigeschwindigkeit) fortbewegen. Diese Geschwindigkeiten sind Parameter der TLL- Theorie und es besteht kein simpler Zusammenhang zwischen ihnen und den Parametern des mikroskopischen Modells, aber durch Ausnutzen der Äquivalenz des TLL Grundzustands mit dem Grundzustand des üblichen Elektronensystems ist es uns möglich, diese Parameter aus mikroskopischen Grundzustandsrechnungen zu extrahieren.
In der vorliegenden Arbeit untersuchen wir die Abhängigkeit der Ladungs- und Spindynamik von der Wechselwirkung in verschiedenen Manifestationen von 1D Fermisystemen. Unser besonderes Interesse gilt dem Spinsektor der, im Gegensatz zur Folklore, von der Wechselwirkung beeinflusst wird. Zu diesem Zweck beschreiben wir die Dynamik des Systems als Tomonaga-Luttinger-Flüssigkeit, während wir für den Grundzustand des Systems Elektronengastechniken verwenden.
In Quantendrähten benutzen wir thermodynamische Relationen um die Plasmon- und Magnongeschwindigkeiten aus dem mikroskopischen Modell zu bestimmen und finden, dass die Leiternäherung (LA) an den Wechselwirkungsvertex eine sehr gute Übereinstimmung mit Quanten-Monte-Carlo Daten liefert und dabei nur einen Bruchteil der Prozessorzeit beansprucht. Andere mean-field Methoden liefern keine vernünftigen Resultate im Spinsektor, obwohl sie im Ladungssektor der LA zum Teil überlegen sind.
Außerdem untersuchen wir das Zusammenspiel zwischen Kontaktwechselwirkung und parabolischem Einschluß in Atomfallen. Es zeigt sich, daß das von Bethe-Ansatz-Rechnungen vorhergesagte Verschwinden der Spingeschwindigkeit (ptoportional zum Quadrat der Teilchendichte) zu einer riesigen Spin-Ladungs-Trennung führt: Ladungsdichtewellen werden am Rand der Falle reflektiert, während Spindichtewellen eine exponentielle Verlangsamung erfahren und nicht reflektiert werden."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Correlated dynamics of quantum wires and cigar shaped atomic gases","Korrelierte Dynamik von Quantendrähten und zigarrenförmigen Atomwolken"]}]}],"canonical_facts":{"dc:contributor":["Grabert, Hermann"],"dc:creator":["Kecke, Lars"],"dc:description.abstract":["In one- dimensional Fermi systems the elementary excitations,as predicted by Tomonaga- Luttinger liquid (TLL) theory, are spin and charge density waves, traveling at different velocities (the spin velocity is smaller, the charge velocity greater than the Fermi velocity). These velocities are parameters of
the TLL theory and there is no straightforward way to extract them from the parameters of a microscopic model.
But by exploiting the equivalence of the TLL ground state with the
usual electron ground state we are able to extract them from
the microscopic model's ground state energy.
In this work we investigate the dependence of charge and spin dynamics
on the interactions in different manifestations of 1D Fermi systems.
We are especially interested in the system's spin sector, which,
contrary to folklore, gets modified by electron- electron interactions.
To do so we describe the system's dynamics in terms of the TLL
while we model the interacting system's ground state with electron gas
techniques.
In quantum wires we use thermodynamical relations to obtain
the plasmon and magnon velocities from the microscopic model
and find out that the ladder approximation (LA) to the
interaction vertex faithfully follows quantum Monte Carlo data while
using a fraction of the processor time; other mean field methods,
although sometimes superior to the LA in the charge sector fail
to give meaningful results in the spin sector.
We also study the interplay of contact interaction and containment in
atomic traps, where we found out that the vanishing spin velocity
(proportional to density squared) at low densities, as predicted from Bethe
ansatz calculation, leads to a giant spin- charge separation; namely
charge density waves get reflected at the system's edge while spin density
waves experience an exponential slowing down and don't get reflected at the
trap edge.","In eindimensionalen Fermisystemen sind die elementaren Anregungen, wie von der Tomonaga-Luttinger-Flüssigkeits (TLL) Theorie vorausgesagt, Spin- und Ladungsdichtewellen die sich mit verschiedenen Geschwindigkeiten (Spindichtewellen langsamer, Ladungsdichtewellen schneller als dire Fermigeschwindigkeit) fortbewegen. Diese Geschwindigkeiten sind Parameter der TLL- Theorie und es besteht kein simpler Zusammenhang zwischen ihnen und den Parametern des mikroskopischen Modells, aber durch Ausnutzen der Äquivalenz des TLL Grundzustands mit dem Grundzustand des üblichen Elektronensystems ist es uns möglich, diese Parameter aus mikroskopischen Grundzustandsrechnungen zu extrahieren.
In der vorliegenden Arbeit untersuchen wir die Abhängigkeit der Ladungs- und Spindynamik von der Wechselwirkung in verschiedenen Manifestationen von 1D Fermisystemen. Unser besonderes Interesse gilt dem Spinsektor der, im Gegensatz zur Folklore, von der Wechselwirkung beeinflusst wird. Zu diesem Zweck beschreiben wir die Dynamik des Systems als Tomonaga-Luttinger-Flüssigkeit, während wir für den Grundzustand des Systems Elektronengastechniken verwenden.
In Quantendrähten benutzen wir thermodynamische Relationen um die Plasmon- und Magnongeschwindigkeiten aus dem mikroskopischen Modell zu bestimmen und finden, dass die Leiternäherung (LA) an den Wechselwirkungsvertex eine sehr gute Übereinstimmung mit Quanten-Monte-Carlo Daten liefert und dabei nur einen Bruchteil der Prozessorzeit beansprucht. Andere mean-field Methoden liefern keine vernünftigen Resultate im Spinsektor, obwohl sie im Ladungssektor der LA zum Teil überlegen sind.
Außerdem untersuchen wir das Zusammenspiel zwischen Kontaktwechselwirkung und parabolischem Einschluß in Atomfallen. Es zeigt sich, daß das von Bethe-Ansatz-Rechnungen vorhergesagte Verschwinden der Spingeschwindigkeit (ptoportional zum Quadrat der Teilchendichte) zu einer riesigen Spin-Ladungs-Trennung führt: Ladungsdichtewellen werden am Rand der Falle reflektiert, während Spindichtewellen eine exponentielle Verlangsamung erfahren und nicht reflektiert werden."],"dc:format.medium":["application/pdf"],"dc:subject":["Luttinger liquid"],"dc:title":["Correlated dynamics of quantum wires and cigar shaped atomic gases","Korrelierte Dynamik von Quantendrähten und zigarrenförmigen Atomwolken"],"dc:type":["DoctoralThesis"]},"updated_at":"2026-07-24T02:22:33Z"}